ADD model

Large extra dimension (ADD model) - 1998

Proposed by Nima Arkani Hamed, Savas Dimopoulos and Gia Dvali: The fields of the Standard Model are confined to a 4-dimensional membrane. Gravity, on the other hand, is free to propagate in the additional spatial dimensions. These extra dimensions are “large” compared to the Planck length. 

Before we proceed, let us remember Newton's inverse-square law of gravity.

The attractive force between two masses is:

• Directly proportional to the product of their masses.

• Inversely proportional to the square of the distance between their centers.

In the ADD model, the particles of the Standard Model are confined to a brane. The ADD models all have more than one extra dimension. These extra dimensions are curled up and large. Depending on the details of the model, there could be 2, 3 or more curled up dimensions. However, the ADD model contains a single brane. This is where the particles of the Standard Model live. The brane does not bound space. However, this brane is embedded in the curled up extra dimensions of space. The question that the ADD model seeks to answer: how could large extra dimensions be hidden, if, all the particles of the Standard Model are trapped on the brane and the only force felt in the higher dimensional bulk is gravity? The result that they stumbled upon was alarming. The size of these extra curled-up dimensions could be the size of a millimeter! This may not seem so big, however, compared to the hundredth of a thousandth of a trillionth of centimeter scale: they're huge. Indeed, a millimeter is huge on the scale of particle physics. Indeed, the search for millimeter sized extra dimensions is on. They have yet to be observed. Based on experiment, these dimensions must be smaller than a tenth of a millimeter. Perhaps they could be detected with a very sensitive gravity probe. However, the thing with gravity, is that, it is very feeble and difficult to detect. For light objects at short distances, gravity is so weak that it is overwhelmed by the other forces. Indeed, gravity is hard to test at short distances. We also know a lot less about it than we do the other forces. Thus, if gravity is the only force in the bulk, than, the existence of large extra dimensions, would not contradict any of our experimental results. 

When these theorists proposed their 1996 paper, Newton's law of gravity had been tested down to the millimeter scale. That being said, there could, potentially, be invisible extra dimensions as large as a millimeter, that no one has ever seen. Experiments of gravity at this scale and lower were just not around at this time. Gravity, very well, could act differently below that scale. Objects could be approaching each other much more rapidly with greater gravitational attraction. How would we know? Indeed, the interest of these theorists was particle physics, and, in particular, the hierarchy problem. The hierarchy problem is concerned with the large difference in mass between: the weak scale mass and the Planck scale energy.

• The weak scale mass: This is where the electroweak symmetry is broken. This is 250 GeV. Particles with energy below this scale, manifest the effects of electroweak symmetry breaking. In other words, the weak bosons and the elementary particles have mass.

• The Planck scale energy: The Planck scale energy is 16 orders of magnitude, greater than the weak scale. This is 10^19 GeV. This Planck scale energy determines the strength of gravitational interactions. Since the force of gravity is small, the Planck scale energy is big. The strength of gravity is inversely proportional to this scale. A smaller fundamental mass scale for gravity would make it far too strong. 

These are the masses that we associate with particles physics and gravity. But the question remains: why is the weak scale mass, so much smaller than the Planck scale energy? Why is the strength of gravity acting on subatomic particles so feeble? Is the nature of gravity, fundamentally different than what physicists had initially assumed? In the ADD model, sufficiently large extra dimensions can answer these questions. What these theorists proposed was that the fundamental mass scale that determines the strength of gravity is not the Planck mass scale. However, it is a much smaller mass scale: about a TeV. 

In the ADD model, the strength of gravity, need only be strong in the higher dimension. The idea is that the large extra dimension could influence the force of gravity to such a degree, that, the force would be strong in the higher dimension, however, feeble in the lower dimension. Gravity would appear weak to us, because of it's interactions with the very large higher dimension. Electromagnetism, the strong and weak nuclear forces, on the other hand, would be confined to the brane, appearing much stronger than gravity, unaltered by the higher dimension. This is an extraordinary implication of the relationship between higher and lower dimensional gravitation. 

How many large extra dimensions are there? If there were only 1, it would have to be huge to be able to diminish the strength of gravity. It would have to be about the size of an AU or astronomical unit (the distance between the Earth and the Sun). There is no way this is the case. If it were, we would be able to observe this 5th dimension with ease. However, with 2 large extra dimensions, the dimensions could be the size of about a millimeter and still have the power to decrease the strength of gravity to what we observe. This is why the millimeter scale is so important to the large extra dimension proposal. When we go beyond 2 extra dimensions in the large extra dimension models, gravity would be modified, only at a very small scale. Even if these dimensions are small, they can still modify the strength of gravity. Perhaps evidence for these small dimensions could be detected in high-energy particle collider experiments.